a rectangular field of fixed area is to be enclosed. It is divided into five lots by parallels to one of the sides. A total of 10,000 meters of fence are available. Find the area of the largest field that can be enclosed.

Question

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Answer 1

as always, split the fence between lengths and widths for maximum area.
If the dimensions are x and y, then
2x+6y = 10000
so the length is 5000/2
and the width is 5000/6
you can go the calculus route by setting
A = xy = x(10000-2x)/6
dA/dx = 0 at x = 2500